1. Field of the Invention
The present invention relates generally to vibration absorbing devices and, more particularly, to a multi-mode vibration absorbing device for implements.
2. Description of the Related Art
The popularity of sports involving implements, such as golf, tennis, hockey and racquet ball, continues at a strong pace. Better engineering, better materials, lighter, stronger implements have improved the play of games with these implements and thereby increased the enjoyment associated therewith. Although these implements have worked well, they suffer from the disadvantage that, despite improvements in other areas, the unwanted vibratory phenomena generated upon an impact with an object which is not dead center in the "sweet spot" of the implement remains.
Lighter implements have allowed players to swing harder at the object. Larger implements, while increasing the "sweet spot" thereof, have also increased the area outside the "sweet spot", providing increased opportunity for imperfect or offset contact with the object.
For example, when an object impacts the implement, the implement excites in a fashion defined by the amount of force, location of impact and the dynamics of the implement structure. The magnitude and location of the impact 6 on the implement 8, as illustrated in FIGS. 1A, 1B and 1C, will cause either one or several modes to excite. Each of these modes will vibrate at a different frequency. The modes excited are the bending mode as illustrated in FIG. 1A, the torsional mode as illustrated in FIG. 1B and the longitudinal mode as illustrated in FIG. 1C. The longitudinal mode may be excited, for example, when the object such as a ball contacts the implement such as a tennis racquet during a serve.
Any excitation is usually expressed as a linear combination of the dynamic modes of the implement as follows: ##EQU1##
where .mu. is the excitation, x.sub.1, x.sub.2, x.sub.3 . . . etc. are the mode shapes and a.sub.1, a.sub.2, a.sub.3, etc. are the coefficients which dictate the contribution of each mode towards the total excitation. In most cases, the energy from the impact excites the first frequency and the spin off energy will excite the second frequency and so on. The most probable modes that are subject to excitation are the first bending mode and first torsional mode. Nevertheless, the other modes get excited when there is enough energy generated during the impact.
Additionally, certain implements such as tennis racquets have increased in length, thereby lowering the natural frequencies of the racquets. For example, the second bending mode of the tennis racquet may have been lowered from five hundred hertz to three hundred hertz for a particular racquet. Thus, there is a need in the art to provide a vibration absorbing device for implements which will effectively damp out the vibrations caused by various modes at various frequencies due to impact.